Conformational Studies of Fluoromethylcyclopropane from

J. Phys. Chem. A 2004, 108, 5353-5364

5353

Conformational Studies of Fluoromethylcyclopropane from Temperature-Dependent FT-IR Spectra of Xenon Solutions and Ab Initio Calculations James R. Durig,* Zhenhong Yu,† Chao Zheng, and Gamil A. Guirgis‡ Department of Chemistry, UniVersity of MissourisKansas City, Kansas City, Missouri 64110 ReceiVed: February 9, 2004; In Final Form: March 30, 2004

Variable-temperature (-55 to -100 °C) studies of the infrared spectra (3500 to 400 cm-1) of fluoromethylcyclopropane, c-C3H5CH2F, dissolved in liquefied xenon have been carried out, and the Raman (liquid and solid) and infrared (gas and solid) spectra have been recorded from 3500 to 60 cm-1. By utilizing four conformer pairs, an enthalpy difference of 262 ( 26 cm-1 (3.13 ( 0.31 kJ/mol) was obtained, with the gauche rotamer the more stable conformer and the only form present in the solid. The abundance of cis conformer present at ambient temperature is 12 ( 1%. On the basis of the far-infrared spectral data along with the experimental enthalpy and gauche dihedral angle, the potential function governing conformational interchange has been obtained, and the determined potential constants are V1 ) -245 ( 23, V2 ) -414 ( 17, V3 ) 1263 ( 6, V4 ) 272 ( 17, and V5 ) 101 ( 2 cm-1, with the cis-to-gauche barrier of 1223 cm-1 (14.63 kJ/mol) and the gauche-to-gauche barrier of 1362 cm-1 (16.29 kJ/mol). From MP2 ab initio calculations with triple-ζ basis sets with diffuse functions, the gauche conformer is predicted to be the more stable rotamer by about 320 cm-1, which is consistent with the experimental results, but without diffuse functions the two conformers are predicted to have nearly the same energy. Similar results are predicted from density functional theory by the B3LYP method. The complete vibrational assignment for the gauche conformer is proposed, and several fundamentals for the cis conformer have been identified. The structural parameters, dipole moments, conformational stability, vibrational frequencies, and infrared and Raman intensities have been predicted from ab initio calculations. These experimental and theoretical results are compared to the corresponding quantities of some similar molecules.

Introduction For some time, the relative stabilities of the rotamers of halomethylcyclopropane1-7 have been investigated along with those of methyl-,8 cyano-,9,10 and ethynyl (acetenyl)substituted11-13 molecules. These compounds are of interest because, for molecules which contain an asymmetrical monosubstituted methyl group bonded to a symmetrical threemembered (cyclopropane) ring, two staggered conformers of cis (syn) and gauche structure are possible, whereas the eclipsed forms have been predicted to be unstable.1-13 The conformational stability of fluoromethylcyclopropane has not been determined experimentally, apparently because of its instability.14 From theoretical investigations, both the cis and gauche rotamers have been predicted to be the more stable conformer.14,15 On the basis of molecular mechanics calculations,15 the cis rotamer was predicted to be the lower energy conformer by 190 cm-1, whereas from MP4(SDQ)/6-311G(d,p) calculations it has been concluded that the gauche (skew) rotamer is more stable by 70 cm-1. For the other three halomethylcyclopropane molecules, the gauche form is predominant in chloromethylcyclopropane,7 with 88% of this conformer present at ambient temperature, the corresponding bromo7 and iodo6 molecules having 92% and 100% gauche form present at * Corresponding author. Phone: (816) 235-6038. Fax: (816) 235-2290. E-mail: [email protected]. † This article is taken in part from the dissertation of Z.Y. which was submitted to the Department of Chemistry in partial fulfillment of the Ph.D. degree. ‡ Present address: Department of Chemistry & Biochemistry, College of Charleston, Charleston, SC 29403.

ambient temperature, respectively, in the gas phase. Thus, it has been proposed6 that as the size of the halogen atom increases, the abundance of the cis conformer decreases. As a continuation of these studies on the effect of the substituent on the monosubstituted methylcyclopropane molecules, spectroscopic and theoretical studies of methyl,8 cyano9,10 and ethynyl12 groups as substituents have been carried out, with the abundance of the gauche conformer in the gas phase at ambient temperature determined experimentally to be 92%, 72%, and 52%, respectively. These experimental results are in good agreement with ab initio calculations from the MP2/6-31G(d) basis set. From a microwave study11 of cyclopropylmethylacetylene (ethynylmethylcyclopropane), the energy difference was determined to be 64 ( 30 cm-1, with the cis conformer more stable; the conformational stability order is in agreement with our more recent experimental result12 of 147 ( 14 cm-1, a significantly larger value obtained from infrared spectra of variable-temperature studies of xenon solutions. Since the values for the electronegativity16 of I, Br, Cl, CH3, CtN, and CtCH are 2.5, 2.8, 3.0, 2.9, 3.2, and 3.1, these investigators11 concluded that the abundance of the cis form parallels the increase of electronegativity of the substituents for the monosubstituted methylcyclopropane molecules. To provide a test of the effect of the electronegativity of the substitution on the monosubstituted methylcyclopropane molecules, a conformational study of fluoromethylcyclopropane became of interest because of the large value of the electronegativity of the fluorine atom. First, ab initio calculations with a variety of basis sets at the level of restricted Hartree-Fock

10.1021/jp0401168 CCC: $27.50 © 2004 American Chemical Society Published on Web 05/28/2004

5354 J. Phys. Chem. A, Vol. 108, No. 25, 2004

Durig et al.

TABLE 1: Calculated Energies (Hartrees) and Energy Differences (cm-1) for the Gauche and Cis Conformers of Fluoromethylcyclopropane method/basis set

gauche

cis

∆Ea

RHF/6-31G(d) RHF/6-31+G(d) RHF/6-311G(d,p) RHF/6-311+G(d,p) MP2/6-31G(d) MP2/6-31+G(d) MP2/6-311G(d,p) MP2/6-311+G(d,p) MP2/6-311G(2d,2p) MP2/6-311+G(2d,2p) MP2/6-311G(2df,2pd) MP2/6-311+G(2df,2pd) B3LYP/6-31G(d) B3LYP/6-31+G(d) B3LYP/6-311G(d,p) B3LYP/6-311+G(d,p) B3LYP/6-311G(2d,2p) B3LYP/6-311+G(2d,2p) B3LYP/6-311G(2df,2pd) B3LYP/6-311+G(2df,2pd)

-254.944445 -254.954936 -255.012959 -255.017639 -255.652957 -255.676310 -255.897879 -255.908546 -255.968529 -255.977076 -256.058669 -256.066621 -256.438232 -256.457763 -256.516844 -256.524640 -256.526255 -256.533134 -256.533157 -256.540001

-254.944824 -254.953779 -255.012695 -255.016433 -255.654060 -255.675171 -255.897857 -255.907089 -255.968488 -255.975584 -256.058631 -256.065145 -256.438902 -256.456178 -256.516797 -256.523019 -256.526201 -256.531558 -256.533111 -256.538396

-83 254 58 265 -242 250 5 320 9 327 8 324 -147 348 10 356 12 346 10 352

Figure 1. Mid-infrared spectra of fluoromethylcyclopropane: (A) gas and (B) annealed solid.

a

Negative value of energy difference indicates that the cis conformer is the more stable form.

(RHF) and with full electron correlation by the perturbation method to second order (MP2) were carried out. These calculations, with basis sets without diffuse functions, predicted the cis form to be the more stable conformer or the two conformers to have nearly the same energy (Table 1). Similar results were also obtained from density functional theory calculations. Since it has been shown17 that ab initio calculations with most of the basis sets with diffuse functions predict the gauche conformer of 3-fluoropropene (allyl fluoride), CH2dCHCH2F, to be the more stable form, whereas the cis rotamer has been experimentally determined18 to be the more stable conformer, the theoretical predictions for fluoromethylcyclopropane cannot be relied on to provide the correct conformer stability. Due to the importance of determining the conformational stability for this molecule, an investigation of fluoromethylcyclopropane from temperature-dependent FT-IR spectra of xenon solutions has been carried out. Additionally, we have recorded the infrared and Raman spectra of the liquid and solid phases. The conformational stability, optimized geometry, force constants, vibrational frequencies, infrared intensities, Raman activities, and depolarization ratios have been calculated for comparison with the experimental quantities when appropriate. The results of these vibrational spectroscopic and theoretical studies are reported herein. Experimental Section The fluoromethylcyclopropane molecule was prepared by the reaction of cyclopropylmethanol with (diethylamino)sulfur trifluoride (DAST), obtained from Aldrich Chemical Co., in diglyme at -50 °C for 1 h. The volatile portion was collected and purified by using a low-temperature, low-pressure fractionation column, and the sample was stored in liquid nitrogen under vacuum until use. The purity of the sample was checked by comparing the mid-infrared spectrum to the ab initio predictions and mass spectral data. All sample transfers were carried out under vacuum to avoid contamination. The mid-infrared spectra (Figure 1) of the gas and the annealed solid from 3500 to 300 cm-1 were recorded on a Perkin-Elmer model 2000 Fourier transform spectrometer equipped with a Nichrome wire source, Ge/CsI beam splitter,

Figure 2. Raman spectra of fluoromethylcyclopropane: (A) liquid and (B) annealed solid.

and DTGS detector. The spectrum of the gas was obtained with the sample contained in a 12 cm cell equipped with CsI windows. Atmospheric water vapor was removed from the spectrometer chamber by purging with dry nitrogen. For the annealed solid, the spectrum was recorded by depositing a solid sample film onto a CsI substrate cooled by boiling liquid nitrogen and housed in a vacuum cell fitted with CsI windows. The sample was annealed until no further change was observed in the spectrum. Interferograms obtained after 256 scans for the gas and reference as well as 128 scans for the amorphous, annealed solid and reference were transformed by using a boxcar truncation function with theoretical resolutions of 0.5 and 1.0 cm-1 for the gaseous and solid samples, respectively. The Raman spectra of fluoromethylcyclopropane from 3200 to 40 cm-1 (Figure 2) were recorded on a SPEX Ramalog spectrophotometer equipped with a Spectra-Physics model 171 argon ion laser operating on the 5145 Å line. The liquid sample was sealed in a glass capillary, and the spectrum was recorded at -10 °C due to the instability of the sample at ambient temperature. The spectrum of the solid was then recorded by inserting the capillary into a Miller-Harvey19 jacket cooled by N2 gas obtained from liquid N2. The temperature of the solid was maintained at about -105 °C by controlling the rate of the nitrogen boiling off from the liquid. The frequencies for the observed lines are listed in Table 1S.

Conformational Studies of Fluoromethylcyclopropane

J. Phys. Chem. A, Vol. 108, No. 25, 2004 5355

Figure 5. Geometric model and internal coordinates for the gauche conformer of fluoromethylcyclopropane.

Figure 3. Far-infrared spectra of fluoromethylcyclopropane: (A) gas, (B) amorphous, and (C) annealed solid.

100 scans at a resolution of 1.0 cm-1. The temperature studies in the liquefied noble gas were carried out in a specially designed cryostat cell, which is composed of a copper cell with a 4 cm path length and wedged silicon windows sealed to the cell with indium gaskets. The temperature was monitored by two Pt thermoresistors, and the cell was cooled by boiling liquid nitrogen. The complete cell was connected to a pressure manifold to allow for the filling and evacuation of the cell. After the cell was cooled to the desired temperature, a small amount of sample was condensed into the cell. Next, the pressure manifold and the cell were pressurized with xenon, which immediately started condensing in the cell, allowing the compound to dissolve. The frequencies observed for the fundamentals are listed in Tables 2 and 3. Ab Initio Calculation

Figure 4. Infrared spectra of fluoromethylcyclopropane: (A) xenon solution at -100 °C, (B) calculated spectrum of the mixture of the two conformers, (C) calculated spectrum of the cis conformer, and (D) calculated spectrum of the gauche conformer.

The far-infrared spectra (600 to 50 cm-1) of the annealed solid (Figure 3C) and gas (Figure 3A) were obtained with the Perkin-Elmer model 2000 Fourier transform spectrometer equipped with a far-infrared grid beam splitter and DTGS detector. The spectrum of the solid was obtained by condensing the sample onto a silicon plate held in a cell equipped with polyethylene windows and cooled with boiling liquid nitrogen at an effective resolution of 1.0 cm-1. The sample was annealed until no further change was observed in the spectrum. The spectrum of the gas was obtained from the sample contained in a 10 cm path cell equipped with polyethylene windows with an effective resolution of 0.5 cm-1. Typically, 256 scans were used for both the sample and reference to give a satisfactory signal-to-noise ratio. The mid-infrared spectra of the sample dissolved in liquefied xenon (Figure 4A) were recorded on a Bruker model IFS-66 Fourier interferometer equipped with a Globar source, Ge/KBr beam splitter, and DTGS detector. The spectra were recorded at variable temperatures ranging from -55 to -100 °C with

The geometry optimization of fluoromethylcyclopropane was performed by the LCAO-MO-SCF restricted Hartree-Fock calculations RHF/6-31G(d) and electron correlation calculations with Møller-Plesset perturbation to the second order, i.e., MP2/ 6-31G(d), MP2/6-311+G(d,p), MP2/6-311++G(d,p), and MP2/ 6-311+G(2d,2p), with the program Gaussian 98 using a Gaussian-type basis set.20 The energy minimum with respect to the nuclear coordinates was obtained by the simultaneous relaxation of all geometric parameters using the gradient method of Pulay.21 These optimized parameters are listed in Table 2S. RHF/6-31G(d) and MP2/6-31G(d) calculations predict the cis conformer to be the more stable rotamer, and even with much larger basis sets the gauche form is favored by only a few wavenumbers, i.e., 5-9 cm-1. However, by using diffuse functions, the gauche form is predicted to be more stable by about 320 cm-1 (Table 1). Similar density functional theory (DFT) calculations by the B3LYP method with the same basis sets predict the same results: without diffuse functions the gauche conformer is predicted to be more stable by about only 10 cm-1. However, the corresponding calculations with basis sets with diffuse functions predict the gauche conformer to be more stable by about 350 cm-1. The intramolecular harmonic force fields were calculated with the Gaussian 98 program at the MP2/6-31G(d) levels. Internal coordinates were defined as shown in Figure 5, and they were used to form the symmetry coordinates listed in Table 3S. The Cartesian coordinates obtained from the optimized geometry were used to calculate the B-matrix elements. These B-matrix elements were used to convert22 the ab initio force fields in Cartesian coordinates to force fields in desired internal coordinates, and the resulting force constants can be obtained from the authors. These force fields were used to reproduce the ab initio vibrational frequencies without a scaling factor. Scaling factors of 0.88 for all of the C-H stretching modes, 0.90 for all the heavy-atom stretches and C-H bending modes, and 1.0


Durig et al.

TABLE 2: Observed and Calculated Frequencies (cm-1) and Potential Energy Distribution for gauche-Fluoromethylcyclopropane vib. no.

fundamental vibration

ab initioa

fixed scaledb

IR int.c

Raman act.c

dp ratio

obsdd

PEDe

ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12 ν13 ν14 ν15 ν16 ν17 ν18 ν19 ν20 ν21 ν22 ν23 ν24 ν25 ν26 ν27 ν28 ν29 ν30

CH2 antisymmetric stretch CH2 antisymmetric stretch C-H stretch CH2 symmetric stretch CH2 symmetric stretch CH2(F) antisymmetric stretch CH2(F) symmetric stretch CH2(F) deformation CH2 deformation CH2 deformation CH in-plane bend CH2(F) wag CH2(F) twist ring breathing CH2 twist CH2 twist CH out-of-plane bend CH2 wag CH2 wag C-F stretch C-C stretch ring deformation CH2(F) rock ring deformation CH2 rock CH2 rock C-F bend ring-CH2F in-plane bend ring-CH2F out-of-plane bend CH2F torsion

3307 3295 3232 3212 3207 3163 3102 1584 1574 1529 1496 1425 1320 1271 1243 1235 1178 1113 1108 1093 1071 989 958 885 846 805 485 363 237 109

3102 3092 3032 3014 3009 2967 2910 1503 1493 1451 1419 1353 1254 1206 1184 1173 1119 1057 1051 1040 1021 940 911 841 804 764 475 356 236 109

11.5 0.4 8.0 6.2 10.6 38.0 35.8 2.2 0.1 2.6 29.7 8.3 1.4 2.0 2.6 0.6 1.2 1.9 24.4 90.5 16.3 9.9 3.0 7.0 2.5 0.6 7.4 0.6 3.4 2.5

36.2 90.2 125.4 104.5 28.9 71.2 85.1 6.6 6.5 7.9 3.0 6.2 7.6 15.6 8.9 9.9 0.7 0.2 1.2 4.2 7.8 12.4 5.4 10.3 7.6 5.9 3.7 0.9 0.06 0.02

0.57 0.74 0.07 0.20 0.52 0.71 0.10 0.72 0.62 0.75 0.59 0.54 0.71 0.20 0.64 0.33 0.73 0.74 0.61 0.70 0.31 0.49 0.74 0.74 0.57 0.61 0.57 0.18 0.70 0.50

3096 3084 3042 3018 3004 2956 2898 1477 1465* 1438 1412 1348 1266 1200 1186 1170* 1099 1053 1042 1025 1010 930 907 834 804 768 477 358 237 113

97S1 98S2 97S3 92S4 93S5 97S6 99S7 70S8, 24S9 51S9, 28S8, 13S14 100S10 21S11, 40S12, 14S21, 13S9 56S12, 19S11 68S13, 12S26 50S14, 28S11 12S15, 31S23, 14S21, 13S11, 10S13 38S16, 46S25, 11S17 60S17, 32S16 79S18 65S19, 16S18, 11S20 68S20, 15S19 16S21, 23S23, 11S24, 10S14 31S22, 25S24 22S23, 23S26, 18S24 39S24, 18S25, 12S22, 10S16, 10S17 17S25, 27S22, 11S21, 11S26 43S26, 45S15 41S27, 22S29 79S28 52S29, 33S27 79S30, 11S29

a Calculated values are obtained by ab initio calculations at the MP2/6-31G(d) level. b Calculated using scaling factors of 0.88 for C-H stretches, 0.90 for C-H bends and heavy atom stretches, and 1.0 for heavy atom bends and torsional mode. c Infrared intensities are in km/mol; Raman activities in Å4/µ. d Frequencies from infrared spectrum of the gas and xenon solutions except for those marked with asterisks, which are from the Raman spectrum of the solid. e Potential energy distribution predicted by ab initio calculations; contributions less than 10% are omitted.

for the heavy-atom bending modes and asymmetric torsion were input along with the force fields into a perturbation program to obtain the “fixed scaled” force field, vibrational frequencies, and potential energy distributions (PEDs). These data are listed in Tables 2 and 3. To aid in the vibrational assignment, the theoretical infrared spectra of both the cis and gauche conformers were calculated as well as spectra of mixtures of the two conformers with various energy differences between them. The infrared intensities were calculated on the basis of the dipole moment derivatives with respect to the Cartesian coordinates. The derivatives were taken from the ab initio calculations transformed to normal coordinates by

( ) ∑( ) ∂µu

∂µu

)

∂Qi

j

Lij

∂Xj

where Qi is the ith normal coordinate, Xj is the jth Cartesian displacement coordinate, and Lij is the transformation matrix between the Cartesian displacement coordinates and normal coordinates. The infrared intensities were then calculated by

Ii )

[( ) ( ) ( ) ]

Nπ ∂µx 3c2 ∂Qi

2

+

∂µy ∂Qi

2

+

∂µz ∂Qi

2

In Figure 4D is shown the predicted infrared spectrum of the more stable gauche conformer, and Figure 4C shows that for the cis conformer. The predicted infrared spectrum of the mixture at -100 °C is shown in Figure 4B with the enthalpy difference of 262 cm-1 (experimentally determined value), with the gauche conformer the more stable rotamer. The experimental

infrared spectrum of fluoromethylcyclopropane dissolved in liquid xenon at -100 °C is also shown for comparison in Figure 4A. The agreement between the observed and calculated spectra is excellent, and these data were quite valuable for making the vibrational assignment. Also to support the vibrational assignment, we have predicted the Raman spectra from the ab initio calculation results. The evaluation of Raman activity using analytical gradient methods has been developed.23,24 The activity Sj can be expressed as

Sj ) gj(45Rj2 + 7βj2) where gj is the degeneracy of the vibrational mode j, Rj is the derivative of the isotropic polarizability, and βj is that of the anisotropic polarizability. The Raman scattering cross sections, ∂σj/∂Ω, which are proportional to the Raman intensities, can be calculated from the scattering activities and the predicted wavenumbers for each normal mode using the relationship25,26

( )(

)( )

(ν0 - νj)4 ∂σj h 24π4 ) S ∂Ω 45 1 - exp[-hcνj /kT] 8π2cν j j where ν0 is the exciting wavenumber, νj is the vibrational wavenumber of the jth normal mode, and Sj is the corresponding Raman scattering activity. To obtain the polarized Raman scattering cross sections, the polarizabilities are incorporated into Sj by multiplying Sj by (1 - Fj)/(1 + Fj), where Fj is the depolarization ratio of the jth normal mode. The Raman scattering cross sections and calculated wavenumbers obtained from the Gaussian 98 program20 were used together with a Lorentzian function to obtain the calculated spectra.



TABLE 3: Observed and Calculated Frequencies (cm-1) and Potential Energy Distribution for cis-Fluoromethylcyclopropane species

vib. no.

fundamental vibration

ab initioa

fixed scaledb

IR int.c

Raman act.c

dp ratio

A′ A′′ A′ A′ A′′ A′′ A′ A′ A′ A′′ A′ A′ A′′ A′ A′ A′′ A′′ A′′ A′ A′ A′ A′ A′′ A′′ A′′ A′ A′ A′ A′′ A′′

ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12 ν13 ν14 ν15 ν16 ν17 ν18 ν19 ν20 ν21 ν22 ν23 ν24 ν25 ν26 ν27 ν28 ν29 ν30

CH2 antisymmetric stretch CH2 antisymmetric stretch C-H stretch CH2 symmetric stretch CH2 symmetric stretch CH2(F) antisymmetric stretch CH2(F) symmetric stretch CH2(F) deformation CH2 deformation CH2 deformation CH in-plane bend CH2(F) wag CH2(F) twist ring breathing CH2 twist CH2 twist CH out-of-plane bend CH2 wag CH2 wag C-F stretch C-C stretch ring deformation CH2(F) rock ring deformation CH2 rock CH2 rock C-F bend ring-CH2F in-plane bend ring-CH2F out-of-plane bend CH2F torsion

3316 3305 3215 3221 3214 3162 3104 1585 1575 1519 1462 1465 1301 1273 1110 1240 1173 1142 1117 1174 1025 807 1142 924 843 832 585 249 350 154

3110 3100 3015 3022 3015 2967 2912 1505 1496 1441 1388 1391 1235 1209 1015 1177 1114 1060 1054 1120 973 765 1089 876 801 790 574 245 348 154

8.0 0.3 9.3 5.2 10.6 40.3 51.6 0.4 0.9 2.6 0.5 20.9 1.6 2.7 5.6 0.4 3.0 0.1 2.8 21.3 43.8 1.2 0.1 9.9 3.0 0.3 6.2 3.6 1.0 2.0

28.7 84.7 25.3 208.6 25.3 81.2 114.4 9.9 4.1 8.1 4.4 5.2 8.0 22.9 0.8 8.9 1.3 0.4 1.0 1.5 12.4 15.7 0.4 17.2 2.2 1.1 1.7 0.2 0.3 0.02

0.75 0.75 0.61 0.06 0.75 0.75 0.13 0.62 0.73 0.75 0.50 0.75 0.75 0.17 0.34 0.75 0.75 0.75 0.75 0.71 0.29 0.53 0.75 0.75 0.75 0.75 0.68 0.17 0.75 0.75

obsdd

3029 2932 2916

1362 1392 1222

1119 1141 965 861 564 243 334 150

PEDe 99S1 99S2 51S3, 48S4 51S4, 48S3 100S5 100S6 100S7 84S8 60S9, 17S14, 15S8 100S10 31S11, 28S12, 24S9 60S12, 19S21 91S13 46S14, 25S11, 13S15 23S15, 33S20, 16S26, 12S11 47S16, 45S25 58S17, 19S16, 15S23 90S18 86S19 44S20, 12S15, 10S11 25S21, 30S22, 12S19, 10S20 40S22, 22S15, 22S21, 11S26 54S23, 15S16, 10S29 86S24, 10S25 42S25, 26S17, 19S16 59S26, 12S15, 12S21, 12S22 48S27, 28S28, 11S15 60S28, 37S27 86S29 9630

a Calculated values are obtained by ab initio calculations at the MP2/6-31G(d) level. b Calculated using scaling factors of 0.88 for C-H stretches, 0.90 for C-H bends and heavy atom stretches, and 1.0 for heavy atom bends and torsional mode. c Infrared intensities are in km/mol; Raman activities in Å4/µ. d Frequencies from infrared spectrum of the gas or xenon solutions. e Potential energy distribution predicted by ab initio calculations; contributions less than 10% are omitted.

Raman spectrum of the liquid is shown in Figure 6A for comparison, and the agreement is considered satisfactory but not nearly as good as the agreement of the simulated infrared spectrum due to the significant extent of intermolecular association in the liquid phase. Vibrational Assignments

Figure 6. Raman spectra of fluoromethylcyclopropane: (A) liquid, (B) calculated spectrum of the mixture of both conformers, (C) calculated spectrum of the cis conformer, and (D) calculated spectrum of the gauche conformer.

The predicted Raman spectra of the pure gauche and cis conformers are shown in Figure 6D and Figure 6C, respectively. In Figure 6B the mixture of the two conformers is shown with the experimentally determined ∆H value of 262 cm-1, with the gauche conformer the more stable form. The experimental

To determine the conformational stability of fluoromethylcyclopropane, it is necessary to correctly identify fundamentals for each conformer. Additionally, the bands chosen for the stability study should not have any accidental fundamentals, overtone, and combination bands of the other conformer at the same frequency. Therefore, the vibrational assignment needs to be made for each conformer, which was aided by the ab initio predictions for the fundamentals. The cis conformer has Cs symmetry, and the fundamental vibrations span the irreducible representation 17A′ + 13A′′. Based on the prediction of structural parameters from ab initio calculations (Table 2S), the c principal axis is perpendicular to the symmetry plane for the cis conformer. Therefore, the out-of-plane modes are expected to give rise to C-type infrared band contours and the in-plane modes should be A, B, or A/B hybrid-type contours. The A′′ vibrations of the cis conformer will yield depolarized Raman lines in the spectrum of the liquid, whereas the A′ vibrations should give rise to polarized Raman lines. The gauche form has C1 symmetry and gives rise to A, B, C, and any hybridtype infrared band contours. The data from the solid phase are also helpful in identifying conformer bands, as only one conformer should remain upon annealing. For fluoromethylcyclopropane, it will be shown that the form in the annealed solid is the gauche conformer, and all of the bands which are

5358 J. Phys. Chem. A, Vol. 108, No. 25, 2004 observed in the fluid phases and disappear in the crystal have been assigned to the cis conformer. Carbon-Hydrogen Modes. In the infrared spectrum of the solid, five pronounced bands were observed at 3089, 3081, 3039, 2968, and 2901 cm-1, as well as one broad band with two maxima at 3016 and 3009 cm-1. Since there should be seven carbon-hydrogen stretching fundamentals for the gauche conformer in this region, and the C-H stretching modes on the ring are predicted to have higher frequencies than those at the CH2(F) group, by comparison to the spectra of similar molecules,2,5,6 the bands at 3089, 3081, and 3039 cm-1 have been assigned as CH2 antisymmetric stretches and C-H stretch with the broad band as CH2 symmetric stretches, and the two bands of medium intensity at 2968 and 2901 cm-1 should be assigned as CH2(F) antisymmetric and symmetric stretches, respectively, which agrees with the predicted wavenumbers and infrared intensities from ab initio calculations. The assignment of the carbon-hydrogen bending modes on the ring for the gauche conformer compares favorably with the corresponding modes of similar molecules. The CH2(F) deformation has been assigned to the highest frequency band at 1436 cm-1 in the region of 1500 to 1300 cm-1 according to the prediction from ab initio calculations. And the CH2(F) wag, CH2(F) twist, and CH2(F) rock have been assigned to the bands observed at 1351, 1269, and 906 cm-1 in the Raman spectrum of the solid, in good agreement with the corresponding modes for 3-fluoropropene at 1367, 1244, and 918 cm-1 from a previous study.18,27 Skeletal Modes. The ab initio calculations predict that the C-F stretch has the highest infrared intensity in the spectrum of the gas of the gauche conformer. Therefore, the strongest band, observed at 1025 cm-1 in the infrared spectrum of the gas, is assigned to this mode, with the C-F bending mode assigned to another strong band at 477 cm-1. For the cis conformer, the C-F bending mode is predicted to be at 555 cm-1 with almost an A-type band contour. Therefore, the A-type band at 564 cm-1 in the infrared spectrum of the gas, which disappeared under annealing, is assigned to this mode. This assignment gives strong evidence that only the gauche conformer remains in the annealed solid. The ring breathing mode for the gauche conformer has been assigned to the strongest band at 1201 cm-1 in the Raman spectrum, which is typical of three-membered-ring molecules. For the other ring modes, the strong Raman lines at 927 and 836 cm-1 in the spectrum of the solid have been assigned to the ring antisymmetric and symmetric deformational modes of the gauche conformer, respectively, consistent with the predictions from the ab initio calculations and the observed frequencies for similar molecules. For the ring-CH2F bending modes, the ab initio calculations predict similar wavenumbers for the two conformers in this lowfrequency region, and the bands in the spectra of the solid have significant shifts toward higher frequency compared to those in the spectra of the fluid phases. For these modes, the infrared band contours become very important for identification of the conformer giving rise to the band. The ring-CH2F in-plane bend for the gauche conformer is expected to be at 356 cm-1 with 95% B-type band contour, and the ring-CH2F out-of-plane bend for the cis conformer is expected to be at 348 cm-1 with a pure C-type band. In the far-infrared spectrum of the gas, a B-type band is observed at 358 cm-1 and assigned as the ring-CH2F in-plane bend for the gauche form, whereas a weak C-type band at 334 cm-1 is assigned as the ring-CH2F out-of-plane bend for the cis rotamer. Similarly, the ring-CH2F out-of-plane bend

Durig et al. TABLE 4: Temperature Dependence and Intensity Ratios from Conformational Study of Fluoromethylcyclopropane T (°C) -55.0 -60.0 -65.0 -70.0 -75.0 -80.0 -85.0 -90.0 -95.0 -100.0

1000/T (K-1) I927g/I961c I904g/I961c I1100g/I1115c 4.584 4.692 4.804 4.922 5.047 5.177 5.315 5.460 5.613 5.775

∆Ha (cm-1)

2.872 2.920 3.051 3.174 3.312 3.445 3.668 3.861 4.055 4.352 250 ( 5

I769g/I565c

2.192 2.251 2.322 2.423 2.548 2.619 2.797 2.911 3.062 3.294

1.052 1.123 1.093 1.253 1.310 1.394 1.458 1.580 1.590 1.694

1.581 1.663

237 ( 5

288 ( 19

272 ( 38

1.837 2.147 1.851 2.063 2.368 2.619

Average value is 262 ( 16 cm (3.13 ( 0.19 kJ/mol), with the gauche conformer the more stable rotamer. a

-1

for the gauche conformer has been assigned to the A-type band at 237 cm-1. Asymmetric Torsions. The ab initio calculations predict the frequencies of the asymmetric torsional mode of the cis and gauche conformers at 154 and 109 cm-1, respectively. A significant series of strong Q-branches are observed at 113.02, 111.52, 109.53, 107.38, 105.13, and 102.78 cm-1, with a weak, sharp Q-branch at 149.78 cm-1 in the far-infrared spectrum of the gas. Because of the relatively large enthalpy difference between the two conformers along with the predicted band contours and intensities, the Q-branches are assigned to the ground-state and first five excited-state transitions of the CH2F torsional mode for the gauche conformer, whereas the Q-branch at 149.78 cm-1 is assigned as the fundamental torsional mode for the cis form. Conformational Stability To obtain the enthalpy difference between the two conformers, the mid-infrared spectra of fluoromethylcyclopropane dissolved in liquefied xenon as a function of temperature from -55 to -100 °C have been recorded. Only small interactions are expected to occur between the dissolved sample and the surrounding xenon atoms, and consequently only small frequency shifts are anticipated when passing from the gas phase to the liquefied noble gas solutions.27-31 A significant advantage of this temperature study is that the conformer bands are better resolved in comparison with those in the infrared spectrum of the gas, and the temperature of the solution is easily maintained for high-accuracy measurements. This is particularly important since most of the conformer bands for this molecule are expected to be observed within a few wavenumbers of each other. Also, the areas of the conformer peaks are more accurately determined than those from the spectrum of the gas. In the xenon solutions of fluoromethylcyclopropane, the major intermolecular force is the dipole-induced dipole interaction between this molecule and surrounding xenon atoms. From ab initio calculations, the dipole moments of the two conformers are predicted to have similar values (Table 2S), and the molecular sizes of the two rotamers are nearly the same, so the ∆H value obtained from the temperature-dependent FT-IR study is expected to be close to the value for the gas.28-32 The bands used for the conformational stability study are those assigned to the CH2 rock at 769 cm-1 (gauche), C-F bend at 565 cm-1 (cis), CH2(F) rock at 904 cm-1 (gauche), ring deformation at 927 cm-1 (gauche), C-C stretch at 961 cm-1 (cis), and CH out-of-plane bend at 1115 (cis) and 1100 cm-1 (gauche). Ten sets of spectral data were obtained for four pairs of conformer bands (Table 4). The intensities of the infrared


J. Phys. Chem. A, Vol. 108, No. 25, 2004 5359 combination bands in near coincidence with the measured fundamentals. A more reasonable uncertainty is at least 10% to provide a more realistic error value. Thus, a final value of 262 ( 26 cm-1 (3.13 ( 0.31 kJ/mol) is reported for the enthalpy difference between the two conformers. Discussion

Figure 7. Temperature dependence of infrared spectra in the region 880-980 cm-1 of fluoromethylcyclopropane.

Figure 8. Temperature dependence of infrared spectra in the region 1080-1130 cm-1 of fluoromethylcyclopropane in xenon solutions.

bands were measured as a function of temperature, and their ratios were determined. By application of the van’t Hoff equation, -ln K ) ∆H/(RT) - ∆S/R, where ∆S is the entropy change, ∆H was determined from a plot of -ln K versus 1/T, where ∆H/R is the slope of the line and K is substituted with the appropriate intensity ratios. It was assumed that ∆H is not a function of temperature in the temperature range studied. From a plot of the natural logarithm of the ratio I769/I565 as a function of the reciprocal of the absolute temperature, the ∆H value was determined to be 272 ( 38 cm-1, with the gauche form the more stable rotamer. Similarly, the pairs of I927/I961, I904/I961, and I1100/I1115 (Figures 7 and 8) gave the ∆H values of 250 ( 3, 237 ( 5, and 288 ( 19 cm-1, respectively, again with the gauche conformer the more stable form (Table 4). The average of these four values is 262 ( 16 cm-1, where the error limit is given by the standard statistical deviation of the measured areas of the intensity data. These error limits do not take into account small associations with the liquid xenon or other experimental factors such as the presence of overtones or

Two scaling factors of 0.88 and 0.90 have been used with the MP2/6-31G(d) calculations to obtain the predicted vibrational frequencies, which are in good agreement with the observed values. The average error in the frequency predictions for the normal modes of the gauche conformers is 8.4 cm-1, which represents a percentage error of 0.6, with the largest errors on the CH2 deformations. Thus, multiple scaling factors are not needed for predicting the wavenumbers of the normal modes aiding in the vibrational assignments for the fundamentals, particularly for distinguishing those for the two different conformers. There are five modes, ν11, ν15, ν21, ν23, and ν25, where the described vibration contributes 22% or less to the atomic motion for the gauche form as indicated by the PEDs (Table 2). These include two of the CH2 rocks, the C-C stretch, the CH2 twist, and the C-H bend, which are vibrations where one usually finds such mixing for the monosubstituted methylcyclopropane molecules, particularly when there are no symmetry elements present. The mixing is less extensive for the cis rotamer, but ν11, ν15, and ν21 still are extensively mixed (Table 3). The major differences in the structural parameters (Table 2S) between the two conformers are those about the CH2F group; for example, the C-F distance for the gauche conformer is predicted to be 0.004 Å longer than that for the cis form. Therefore, it is reasonable to expect that there will be significant differences in the normal-mode frequencies between the two conformers for those fundamentals involving the CH2F group. The C1-C4 distance for the cis conformer is predicted to be 0.010 Å longer than that for the gauche conformer; accordingly, the stretching force constant for this mode is larger by about 10% for the gauche conformer than the corresponding force constant for the cis form. As a result, the C1-C4 stretching mode (ν21) is observed at 1010 cm-1 for the gauche conformer and shifts to 965 cm-1 for the cis form. However, the largest differences in the force constants are the bending force constants associated with the CH2F group; for example, the bending force constant for the CCF angle () increases by 30% when the angle increases by only 0.4° for the cis conformer. For this reason, the CCF bending mode shifts from 477 cm-1 for the gauche rotamer to 564 cm-1 for the cis conformer. Another large difference is found in the torsional force constant (τ), which increases by 50% for the cis conformer and results in the torsional fundamental frequency shifting from 113 cm-1 for the gauche conformer to 150 cm-1 for the cis form. Because of the structural parameter change of the CH2F group, all the normal modes associated with this group have some remarkable shifts between the conformers. In fact, for the gauche conformer, the CH2(F) wag and twist modes have been assigned to the bands at 1348 and 1266 cm-1, whereas the corresponding modes for the cis conformer are found at 1392 and 1222 cm-1, respectively. Therefore, the bending modes are much more indicative of the presence of the conformers for these types of molecules than the stretching modes. For fluoromethylcyclopropane, molecular mechanics calculations indicated that the cis conformer is the more stable rotamer.15 From the present study of the vibrational spectra of the fluid and solid phases, the gauche conformer has been


Durig et al.

TABLE 5: Observed Asymmetric Torsional Transitions of Fluoromethylcyclopropane transition gauche -1 r (0 (2 r -1 -3 r (2 (4 r -3 -5 r (4 (6 r -5 cis 1r0

obsd (cm-1)

calcda (cm-1)

∆ (cm-1)

113.02 111.52 109.53 107.38 105.13 102.78

113.10 111.39 109.51 107.45 105.20 102.72

0.08 -0.13 -0.03 0.07 0.07 -0.05

149.78

149.78

0.00

Calculated using F0 ) 1.426842, F1 ) 0.018681, F2 ) 0.013713, F3 ) -0.000816, F4 ) 0.000108, F5 ) -0.000010 cm-1. a

identified as the more stable form in all three physical states. The enthalpy value determined from the xenon solutions is consistent with the ab initio calculations with diffuse functions. However, the RHF/6-31G(d) and MP2/6-31G(d) ab initio calculations predict the cis conformer to be the more stable form by 83 and 242 cm-1, respectively. Also, it should be noted that the MP2 calculations without diffuse functions give the gauche more stable than the cis form by only a few wavenumbers (5-9 cm-1 from the 6-311G(d,p) to 6-311(2df,2pd) basis sets). Similar results were obtained from the B3LYP calculations, where with the larger basis sets without diffuse functions the gauche conformer is predicted to be more stable than the cis form by only 10-12 cm-1. With the assignment of the torsional fundamental for the gauche conformer along with several excited-state transitions as well as the torsional fundamental of the cis form, it is possible to obtain the experimental potential function governing the conformational interchange. The torsional potential is represented by a Fourier cosine series in the internal rotation angle θ: 6

V(θ) )

((Vi /2))(1 - cos iθ) ∑ i)1

where θ and i are the torsional angle and foldedness of the barrier, respectively. The potential coefficients V1 through V6 were initially calculated from the input of the frequencies for the two torsional transitions, the experimental ∆H value, the gauche dihedral angle, and the internal rotation kinetic constant, F(φ). The internal rotation constant also varies as a function of the internal rotation angle, and it is approximated by another Fourier series: 6

F(φ) ) F0 +

Fi cos φ ∑ i)1

The relaxation of the structural parameters, B(φ), during the internal rotation can be incorporated into the above equation by assuming them to be small periodic functions of the torsional angle of the general type

B(φ) ) a + b cos φ + c sin φ The series approximating the internal rotation constants for fluoromethylcyclopropane were determined by using structural parameters from the MP2/6-311+G(d,p) ab initio calculations. In the initial calculation of the potential parameters, the transitions assigned as the 1 r 0 transition for the cis form and the (1 r -0 transition for the gauche form (Table 5) were used with the value of 262 cm-1 for ∆H and a dihedral angle of 113.7° for the gauche rotamer. As the values for the potential

Figure 9. Asymmetric torsional potential function for fluoromethylcyclopropane, with the dark solid curve the experimentally determined potential function, the thin solid curve from MP2/6-31+G(d) calculations, and the dotted curve from B3LYP/6-31+G(d) calculations. Torsional dihedral angle of 0° corresponding to the cis conformer.

parameters converged, five additional torsional transitions for the gauche rotamer were added to the calculation. However, it was soon learned that the V6 term was very small and the uncertainty was larger than its value. Therefore, the V6 term was dropped, and the final potential function was obtained with reliably small uncertainties for each of the terms. The final resulting values for the potential coefficients are listed in Table 6, and the potential function is shown in Figure 9. The MP2 calculations with the 6-31G(d) basis set were used to predict the potential surface for conformational interchange. The dihedral angle of the internal rotation for the CH2F moiety was allowed to vary every 30° increment, while the structural parameters were optimized at each position. From the resulting potential surface, only two minima (gauche and cis positions) were predicted, and the maxima correspond to the transition states of interconversion between the two stable conformers. The barriers predicted from those calculations were 929, 1179, and 1572 cm-1 for the cis-to-gauche, gauche-to-cis, and gaucheto-gauche transitions, respectively, with the transition states at the dihedral angles of 53.0° and 180.0°, respectively. The experimentally determined barriers are as follow: cis-to-gauche barrier, 1223 cm-1; gauche-to-cis barrier, 1465 cm-1; and gauche-to-gauche barrier, 1362 cm-1. The values for the coefficients are V1 ) -245 ( 23 cm-1, V2 ) -414 ( 17 cm-1, V3 ) 1263 ( 6 cm-1, V4 ) 272 ( 17 cm-1, and V5 ) 103 ( 2 cm-1. The relatively large values of the V2, V4, and V5 terms indicate that the asymmetric torsional mode of fluoromethylcyclopropane is not a restricted harmonic motion, probably because of the highly nonspherical electron distribution caused by the three-membered ring. From the vibrational study of 3-fluoropropene,18 V1 and V3 were determined to be -162 ( 9 and 860 ( 5 cm-1, while the cis-to-gauche, gauche-to-cis, and gauche-to-gauche barriers were determined to be 1117, 958, and 526 cm-1, respectively (Table 6). The large difference in the gauche-to-gauche barriers between the two molecules indicates that there is a much stronger attractive interaction between the fluorine atom and the vicinal hydrogen atom in fluoromethylcyclopropane than in 3-fluoropropene. It is interesting to compare the potential function of fluoromethylcyclopropane to that of difluoromethylcyclopropane (Table 6).36 The potential function coefficients of V1, V2, and V3 difluoromethylcyclopropane were determined to be 229 ( 5, 40 ( 4, and 1270 ( 3 cm-1, respectively. The difference in the conformational stability between the two molecules gives rise to different V1 and V2



TABLE 6: Potential Function Coefficients (cm-1) for the Asymmetric Torsion of Fluoromethylcyclopropane and Barriers to Interconversion (cm-1)

a

coefficients

experimental valuea

MP2/6-31+G(d)

V1 V2 V3 V4 V5 V6 gauche dihedral angle (°) ∆H (∆E) (cm-1) cis-to-gauche barrier gauche-to-cis barrier gauche-to-gauche barrier

-245 ( 23 -414 ( 17 1263 ( 6 272 ( 17 101 ( 2 113.7 262 ( 16 1223 1465 1362

42 -494 1190 46 90 -48 115.2 250 929 1179 1572

CH2dCHCH2Fb -162 ( 9 333 ( 12 860 ( 5 65 ( 2 -13 ( 5 -35 ( 2 124.6 -130 ( 25 1117 958 526

c-C3H5CHF2c 229 ( 5 40 ( 4 1270 ( 3 -136 ( 2 121.6 -102 ( 8 1255 1155 1399

Calculated using the F numbers given in Table 7. b Reference 34. c Reference 35.

terms. The V3 term, which is the dominating term in the barrier to conformer interconversion, indicates clearly that substitution of the second fluorine atom for hydrogen in the CH2F group of fluoromethylcyclopropane has little effect on the barrier, as was previously found for 1,1-difluoroethane.37 According to a previous theoretical study of internal rotation potential functions,38 the V1 term is related to a simple dipoledipole interaction, which for fluoromethylcyclopropane favors the trans form, having the opposed dipole compared to the cis form with reinforced dipoles. As to the V2 term, it involves σ electron withdrawal and π electron donation.39 In this case, attraction of electrons along the C-F bond partially empties the carbon 2p orbitals and thus facilitates donation from the corresponding 2p orbital of the nearby carbon atoms on the ring. From Walsh’s molecular orbital theory on cyclopropane,33 there should be a preference for the C-F bond to be coplanar with the axis of the 2p orbital of the carbon atom on the ring rather than perpendicular to it. Accordingly, we find a relatively large value of V2 for fluoromethylcyclopropane, and it is probably for this reason that this molecule has an enthalpy difference similar to that for chloromethylcyclopropane. Due to the relative steric interaction of the hydrogen and fluorine atoms with the three-membered ring, the gauche conformer would be expected to be more stable than the cis form for fluoromethylcyclopropane. The enthalpy differences of chloromethylcyclopropane and bromomethylcyclopropane are reported7 to be 274 ( 21 and 383 ( 29 cm-1, respectively, with the gauche rotamer the more stable form for both molecules. Since the enthalpy differences increase with decreasing electronegativity of the halogen atom, it is predicted11 that the cis conformer would be more stable than the gauche form for fluoromethylcyclopropane. However, according to the present study, this prediction is found to be in error. Therefore, the steric effect may be one of the main reasons that the gauche conformer is favored for the halomethylcyclopropanes. On the basis of Walsh-Hoffmann theory,33-35 the corresponding ethylenic molecules are frequently compared to the three-membered-ring molecules, and consequently the conformational stability of 3-fluoropropene, CH2dCHCH2F, is of interest for comparison with the results of fluoromethylcyclopropane. The enthalpy for 3-fluoropropene from the xenon solutions has been determined18 to be 60 ( 8 cm-1, with the cis conformer the more stable rotamer. This result should be contrasted to the theoretical predictions17 for 3-fluoropropene, where the predicted stability from ab initio calculations from basis sets with diffuse functions gives mainly the gauche conformer as the more stable rotamer, whereas the experimentally determined more stable conformer is the cis form,18 with values ranging from 60 ( 8 cm-1 in liquid xenon to 81 ( 1 cm-1 in liquid argon. On the basis of these results, the ab initio

TABLE 7: Calculated Energies (Hartrees) and Energy Difference (cm-1) for the Cis and Gauche Conformers of Cyanomethylcyclopropane method/basis set

cis

gauche

∆Ea

MP2/6-31G(d) MP2/6-31+G(d) MP2/6-311G(d,p) MP2/6-311+G(d,p) MP2/6-311G(2d,2p) MP2/6-311+G(2d,2p) MP2/6-311G(2df,2pd) MP2/6-311+G(2df,2pd) B3LYP/6-31G(d) B3LYP/6-31+G(d) B3LYP/6-311G(d,p) B3LYP/6-311+G(d,p) B3LYP/6-311G(2d,2p) B3LYP/6-311+G(2d,2p) B3LYP/6-311G(2df,2pd) B3LYP/6-311+G(2df,2pd)

-248.654934 -248.668826 -248.879396 -248.885680 -248.944098 -248.949336 -249.039464 -249.043722 -249.449442 -249.459403 -249.517131 -249.520432 -249.525674 -249.529045 -249.533967 -249.537006

-248.654234 -248.668644 -248.878587 -248.885221 -248.943173 -248.948725 -249.038432 -249.043000 -249.449720 -249.460125 -249.517528 -249.521072 -249.525951 -249.529635 -249.534276 -249.537607

154 40 178 101 203 134 226 158 -61 -158 -87 -140 -61 -129 -68 -132

a Negative value of energy difference indicates that the gauche conformer is the more stable form.

calculations should be carried out with relatively larger basis sets with diffuse functions for substituted three-membered rings, but the conformational stability should be determined experimentally when the predicted energy differences are small. To further demonstrate the need for diffuse functions for the ab initio predictions of the conformational stabilities of the monosubstituted methylcyclopropane molecules, we carried out calculations to estimate the conformer stability of cyanomethyland ethynylmethylcyclopropane with a variety of basis sets at the MP2 level and by density functional theory by the B3LYP method with the same basis sets. The predicted energy differences for the c-C3H5CH2CN molecule are listed in Table 7, and those for the c-C3H5CH2CtCH molecule are listed in Table 8. For both of these molecules, the predicted energy differences between the two rotamers give the cis conformer to be the more stable form from the MP2 calculations, with energy differences of approximately 130 cm-1 for the cyano molecule and 175 cm-1 for the ethynyl molecule when diffuse functions are used and about 70 cm-1 larger without diffuse functions. The predicted value agrees well with the experimentally determined value of 147 ( 14 cm-1 (1.76 ( 0.17 kJ/mol) for c-C3H5CH2CtCH, which was obtained from infrared spectra from variable-temperature xenon solutions.12 However, similar experimental studies10 for the cyanide gave the gauche conformer more stable by 54 ( 4 cm-1 (0.65 ( 0.05 kJ/mol), which was consistent with the results from an earlier microwave investigation.40 Therefore, differences between the isoelectric CtCH and CtN groups do not appear to be predicted from the MP2 calculations with basis sets up to 6-311+G(2df,2pd).


Durig et al.

TABLE 8: Calculated Energies (Hartree) and Energy Difference (cm-1) for the Cis and Gauche Conformers of Ethynylmethylcyclopropane method/basis set

cis

gauche

∆Ea

MP2/6-31G(d) MP2/6-31+G(d) MP2/6-311G(d,p) MP2/6-311+G(d,p) MP2/6-311G(2d,2p) MP2/6-311+G(2d,2p) MP2/6-311G(2df,2pd) MP2/6-311+G(2df,2pd) B3LYP/6-31G(d) B3LYP/6-31+G(d) B3LYP/6-311G(d,p) B3LYP/6-311+G(d,p) B3LYP/6-311G(2d,2p) B3LYP/6-311+G(2d,2p) B3LYP/6-311G(2df,2pd) B3LYP/6-311+G(2df,2pd)

-232.560629 -232.574664 -232.787134 -232.792227 -232.849579 -232.853676 -232.943338 -232.946542 -233.348014 -233.358710 -233.414566 -233.416925 -233.423332 -233.425729 -233.431476 -233.433527

-232.559479 -232.574298 -232.786029 -232.791476 -232.848444 -232.852881 -232.942117 -232.945624 -233.347806 -233.359306 -233.414782 -233.417449 -233.423530 -233.426261 -233.431734 -233.434080

252 80 243 165 249 174 268 201 46 -89 -47 -115 -43 -117 -57 -121

a Negative value of energy difference indicates that the gauche conformer is the more stable form.

From the density functional B3LYP calculations with all of the basis sets (except 6-31G(d)), the predictions are that the gauche conformer is the more stable form for both the cyano and ethynyl molecules. Only small differences are predicted in the values with successively larger basis sets, and the difference with diffuse functions is about 60 cm-1, with those with the diffuse functions having the larger values of about 130 cm-1 for the cyano and about 120 cm-1 for the ethynyl molecule, with the gauche conformer the more stable form. This result is in contrast to the predictions from the MP2 calculations, where the cis form was predicted to be more stable. Therefore, the DFT calculations do not predict significant differences in conformer stabilities between the cyanide and ethynyl molecules. At this point it does not appear possible to predict the conformational stability of the monosubstituted methylcyclopropanes from either MP2 or B3LYP calculations if the energy differences between the conformers are less than 200 cm-1. We41 have recently shown that MP2/6-311+G(d,p) calculations predicted the r0 structural parameters for more than 50 carbon-hydrogen distances better than 0.002 Å compared to the experimentally determined values from isolated CH stretching frequencies, which were compared42 to previously determined values from earlier microwave studies. It has also been shown43 that similar calculations predict the C-C distances very well for cyclopropane and methylcyclopropane. Finally, we have found18 that we can obtain good structural parameters by adjusting the structural parameters obtained from the ab initio calculations to fit the rotational constants (computer program A&M, Ab initio and Microwave, developed in our laboratory) obtained from the microwave experimental data. To reduce the number of independent variables, the structural parameters are separated into sets according to their types. Bond lengths in the same set keep their relative ratio, and bond angles and torsional angles in the same set keep their differences in degrees. This assumption is based on the fact that the errors from ab initio calculations are systematic. Therefore, it should be possible to obtain “adjusted r0” structural parameters for c-C3H5CH2CtCH from the six previously reported rotational constants as well as those for the corresponding cyanide, particularly since the distance of the triple bond is nearly the same irrespective of the substituent.44 Such parameters are expected to be more accurate than those obtained from the electron diffraction study45 with microwave rotational constant11 restraints.

The adjusted r0 parameters for the ethynyl molecule obtained by the ab initio MP2/6-311+G(d,p)-predicted parameters and the fit of the six microwave rotational constants11 are listed in Table 9, along with the ab initio values and those reported from the electron diffraction study.45 First, it should be noted that the parameters reported for the heavy atoms, except for the triple bond obtained from the ED investigation, have very large uncertainties, with those for the two carbon distances from the methylene (CH2) moiety and the C2-C3 distance in the threemembered ring being exceptionally large, ranging from 0.013 to 0.028 Å. The adjusted r0 distances for these parameters certainly do not exceed 0.005 Å as uncertainties and are probably slightly less. Also, the previously reported C-H distances for the “ring” bonds, with values of 1.107 ( 0.006 Å, are significantly longer than the methylene C-H distances of 1.095 ( 0.005 Å, which are inconsistent with the shorter C-H bonds for those on the three-membered rings, with the r0 values of 1.084-1.086 ( 0.002 Å, consistent with the expected values. The heavy-atom angle parameters previously reported45 have very small uncertainties, and they agree very well with the r0 parameters for these angles found in this study, whereas the ∠HCH values given earlier have rather large uncertainties (2.4°), whereas the r0 values should be accurate to (0.5° or better. Thus, it is believed that the adjusted r0 parameters obtained from the combined ab initio predicted values and the microwave data for ethynylmethylcyclopropane11 are much more accurate and reliable than the parameters previously reported for this molecule. For the cyanide, since only three experimental rotational constants are available for structural determinations for the gauche conformer, the CtN bond distance was fixed at the value of 1.159 Å from this bond distance in methyl cyanide.46 The fit of the rotational constants is better than 1 MHz, and the determined parameters similar to those of the ethynyl molecule differ by only very small amounts, i.e., 0.002 Å or less. The major parameter to note for both of these molecules is the C1-C4 distance, which is a very short distance of 1.465 Å for the gauche conformer of the sCtCH molecule (1.467 Å for the cyanide) and an even shorter value of 1.463 Å for the cis form. This is in contrast to the ab initio predicted C1-C4 distance in fluoromethylcyclopropane of 1.492 Å for the gauche conformer and the much longer value of 1.502 Å for this bond in the cis form. Similarly, much longer C1-C4 distances have been obtained43 for chloromethylcyclopropane (1.495 Å for the gauche form and 1.507 Å for the cis form). For ethylcyclopropane, where the substitution is a methyl group, the C1-C4 distance is even longer, with values47 of 1.510 Å for the gauche form and 1.518 Å for the cis rotamer. For this latter molecule, the methyl group has a relatively small electronegativity compared to the chlorine atom but similar van der Waals radii, but both have small amounts of the cis conformer present at ambient temperature. Therefore, the electronegativity must have a very minor effect on the amount of the cis form present in these monosubstituted methylcyclopropanes, which is in contrast to the previous suggestion11,45 that electronegativity a major factor for determining the conformational stability of these molecules as well as an earlier suggestion for similar cyclobutanes.48,49 The current results for fluoromethylcyclopropane, coupled with those for the corresponding ethynyl and cyanide analogues, strongly indicate that the major factor contributing to the large amount of the cis conformer present at ambient temperature for these molecules is through-bond interactions between the substituent and the carbon bond to the threemembered ring. This results in a shortening by 0.030 Å or more



TABLE 9: Structural Parameters (Bond Lengths in Angstroms, Angles in Degrees), Rotational Constants, Dipole Moments, and Energies for Substituted Methylcyclopropane Molecules c-C3H5CH2CtCH MP2/6-311+G(d,p) parameter

gauche

cis

r(C1-C2) r(C1-C3) r(C2-C3) r(C1-C4) r(C4-C5) r(C5tC6,N6) r(C1-H1) r(C4-H2) r(C4-H3) r(C2-H4) r(C3-H5) r(C2-H6) r(C3-H7) r(C6-H8) ∠C3C1C2 ∠C1C2C3 ∠C1C3C2 ∠C3C1C4 ∠C1C4C5 ∠C4C5C6,N6 ∠H4C2H6 ∠H5C3H7 ∠H2C4H3 ∠H1C1ring ∠C4C1ring τC4C1C3C2 τC3C1C4C5 τC5C4C1H1 |µa| (D) |µb| (D) |µc| (D) |µt| (D) A (MHz) B (MHz) C (MHz)

1.507 1.505 1.513 1.515 1.464 1.219 1.086 1.097 1.096 1.085 1.085 1.084 1.083 1.064 60.3 59.8 59.9 118.9 111.9 179.1 115.0 115.1 106.8 121.1 124.2 109.1 151.6 63.0 0.733 0.331 0.033 0.805 10545.6 2001.8 1817.4

1.506 1.506 1.513 1.521 1.463 1.219 1.086 1.097 1.097 1.084 1.084 1.084 1.084 1.065 60.3 59.9 59.9 121.0 113.2 179.3 115.6 115.6 107.0 120.2 126.5 110.4 35.9 180.0 0.407 0.575 0.704 6835.0 2650.4 2283.8

MW + EDa

c-C3H5CH2CtN adjusted r0

MP2/6-311+G(d,p)

adjusted r0

cis

gauche

cis

gauche

cis

gaucheb

cisc

1.506(14) 1.509(9) 1.516(14) 1.517(28) 1.450(13) 1.215(3) 1.107(6) 1.095(5) 1.095(5) 1.107(6) 1.107(6) 1.107(6) 1.107(6) 1.065(5) 60.4(3) 59.9(3) 59.7(3) 118.9(17) 114.1(8) 180.0 117.2(24) 117.2(24) 111.6(33) 121.7(33) 123.5(26) 107.7(24) 149.6(16) 61.3(17)

1.509(9) 1.509(9) 1.517(14) 1.518(28) 1.450(13) 1.215(3) 1.107(6) 1.095(5) 1.095(5) 1.107(6) 1.107(6) 1.107(6) 1.107(6) 1.065(5) 60.3(2) 59.9(1) 59.8(1) 121.0(7) 114.1(8) 180.0 115.5(24) 115.5(24) 106.9(33) 120.2(25) 126.5(9) 110.4(19) 35.9(4) 180.0

1.507(5) 1.505(5) 1.513(5) 1.516(5) 1.465(5) 1.209(3) 1.086(2) 1.097(2) 1.096(2) 1.085(2) 1.085(2) 1.084(2) 1.083(2) 1.064(2) 60.3(3) 59.8(3) 59.9(3) 119.2(5) 112.1(5) 178.9(5) 115.0(5) 115.1(5) 106.8(5) 121.1(5) 124.3(5) 108.9(5) 153.6(5) 61.0(5)

1.505(5) 1.505(5) 1.513(5) 1.522(5) 1.463(5) 1.210(3) 1.086(2) 1.097(2) 1.097(2) 1.084(2) 1.084(2) 1.084(2) 1.084(2) 1.065(2) 60.3(3) 59.9(3) 59.9(3) 121.2(5) 113.8(5) 179.5(5) 115.6(5) 115.6(5) 107.0(5) 120.2(5) 126.8(5) 110.6(5) 36.0(5) 180.0

1.506(5) 1.506(5) 1.512(5) 1.519(5) 1.463(5) 1.160(3) 1.086(2) 1.096(2) 1.096(2) 1.084(2) 1.084(2) 1.083(2) 1.083(2) 60.2(3) 59.9(3) 59.9(3) 121.4(5) 112.9(5) 178.9(5) 115.4(5) 115.4(5) 107.6(5) 120.5(5) 127.0(5) 110.7(5) 36.0(5) 180.0

6895.8(5) 2621.43(1) 2268.91(1)

10690.5 1984.9 1808.5

6895.1 2621.7 2269.0

1.506 1.506 1.513 1.519 1.463 1.174 1.086 1.096 1.096 1.084 1.084 1.083 1.083 60.3 59.9 59.9 121.0 112.3 178.6 115.4 115.4 107.6 120.5 126.6 110.4 35.9 180.0 3.156 2.841 4.246 6944.6 2705.4 2337.2

1.507(5) 1.506(5) 1.511(5) 1.514(5) 1.467(5) 1.159(3) 1.085(2) 1.096(2) 1.095(2) 1.085(2) 1.085(2) 1.083(2) 1.083(2) 60.2(3) 59.8(3) 60.0(3) 118.8(5) 111.7(5) 178.8(5) 115.1(5) 115.0(5) 107.3(5) 121.3(5) 124.1(5) 108.5(5) 152.6(5) 62.2(5)

10690.7(11) 1984.990(5) 1808.226(6)

1.506 1.505 1.512 1.514 1.466 1.174 1.085 1.096 1.095 1.085 1.085 1.083 1.083 60.3 59.9 59.8 118.8 111.5 178.9 115.1 115.0 107.3 121.3 123.9 108.6 150.9 63.9 4.043 1.882 0.306 4.471 10670.7 2026.0 1840.8

10800.5 2014.8 1835.9

7019.6 2674.6 2322.0

gauche

a Reference 45. b Microwave rotational constants for gauche-c-C3H5CH2CtN: A ) 10800.703 ( 1.639 MHz, B ) 2014.942 ( 0.006 MHz, C ) 1835.685 ( 0.006 MHz. Dipole moments: |µa| ) 3.77(3) D, |µb| ) 0.63(19) D, |µc| ) 0.72(8) D, |µt| ) 3.89(8) D.40 c Estimated parameters; no microwave data for cis-c-C3H5CH2CtN have been published.

of the C1-C4 bond compared to the corresponding bond in the fluoride and an even larger difference for the chloride and methyl substituents (ethylcyclopropane). A similar effect is also expected for the corresponding molecules where the halogen atom is replaced by a pseudo-halogen substituent, such as NCO or NCS, and a study of one or both of these molecules would be of interest for comparison. A conformational stability study of 2-butynylcyclopropane, where the H atom on the triple bond of ethynylmethylcyclopropane is replaced by a methyl group, would also be of interest, because this molecule would be expected to have the cis form more stable if the primary controlling factor is the C1-C4 distance from the through-bond interaction. Acknowledgment. J.R.D. acknowledges the University of Missouri-Kansas City for a Faculty Research Grant for partial financial support of this research. Supporting Information Available: Table 1S, observed infrared and Raman frequencies for fluoromethylcyclopropane; Table 2S, calculated structural parameters, rotational constants, dipole moments, and energies for fluoromethylcyclopropane; and Table 3S, symmetry coordinates for fluoromethylcyclopropane. This material is available free of charge via the Internet at http://pub.acs.org.

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Conformational Studies of Fluoromethylcyclopropane from

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